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Curves with Two Pencils and Associated Maps to Projective Spaces

Curves with Two Pencils and Associated Maps to Projective Spaces

Abstract Let ๐‘‹ be a smooth and connected projective curve. Assume the existence of spanned ๐ฟ โˆˆ Pic ๐‘Ž (๐‘‹), ๐‘… โˆˆ Pic ๐‘ (๐‘‹) such that โ„Ž 0 (๐‘‹, ๐ฟ) = โ„Ž 0 (๐‘‹, ๐‘…) = 2 and the induced map ฯ• ๐ฟ,๐‘… : ๐‘‹ โ†’ ๐ 1 ร— โ€ฆ